The present invention concerns an apparatus for severing a fibre layer (3) composed of mutually slidable staple fibres, and containing two driven pairs of rolls (9/10; 11/12) forming two nip lines for the fibre layer (3) guided therebetween. Severing is achieved in that the two pairs of rolls (9/10; 11/12) are kinematically coupled using a flexible power transmitting element (19) in such a manner that by moving a roll tandem (26) contained in the path of movement of the power transmitting element (19) one pair of rolls (11/12) is rotated relative to the other one (9/10). Owing to this relative rotation of the pairs of rolls the fibre layer clamped between the nip lines is severed. This apparatus presents the advantage that its design is simple and reliable and that, in particular, no clutch is required.